Hardware & Software System

The logical OR operation between two Boolean variables A and B, given as Y= A+, is represented by table. This table shows the result of the OR operation on the variable A and B is logical 1 when A or B (or both) are logical 1. The common symbol used for this logical addition operation is the plus sign (+).

The logical AND operation of two Boolean variables A and b, given as Y=A, is represented by table. The common symbol for this operation is the multiplication sign (.). The table shows that the result of the AND operation on the variables A and B is logical 0 for all cases, except when both A and B are logical 1. Usually, the dot denoting the AND function is omitted and A.B is written as AB.

A Boolean function is an expression formed using binary constants, binary variable and basic logical operation symbols. Basic logical operations include the AND function (logical multiplication), the OR function (logical addition) and the NOT function (logical Complementation ), A Boolean function can be converted into a logical diagram composed of the AND, OR and NOT gates.

Mathematician George Boole invented a new kind of algebra, the algebra of logic in the year 1854 popularly known as Boolean Algebra or Switching Algebra. He stated that symbols can be used to represent the structure of logical thought. Boolean algebra differs significantly from conventional algebra. This algebra deals with the rules by which the logical operations are carried out. here, a digital circuit is represented by a set of input and output symbols and the circuit functions expressed as a set of Boolean relationships between this symbols.            Boolean expressions are basically defined by stating that (i) a constant is a Boolean expression and (ii) a variable is a Boolean expression. For example, if A is a Boolean expression, so is A bar. The combination of variables such as A bar B and A bar B+C are also Boolean expressions. However, A-B is not a Boolean expression.